Engineering Mechanics

(^460) „„„„„ A Textbook of Engineering Mechanics
Example 22.2. Three links are hinged together to form a triangle ABC as shown in Fig. 22.4.
Fig. 22.4.
At a certain instant, the point A is moving towards the mid-point of BC with a velocity of 5 m/s,
and B is moving at a perpendicular direction to AC. Find the velocity of C.
Solution. Given : Velocity of A (vA) = 5 m/s
First of all, let us locate the position of instantaneous centre of the points A and B graphically
as shown in Fig. 22.5 and as discussed below :

1. Draw the triangle ABC with the given data.


2. Now draw the lines indicating the directions of
   motions of points A (towards mid-point of BC) and
   B (at right angles to AC).


3. Now draw perpendiculars at A and B on the
   directions of motion of vA and vB.


4. Let these perpendiculars meet at O, which is the
   instantaneous centre of the link AB and BC.


5. Now join OC and draw a line at right angle to OC
   indicating the direction of motion of the point C.
   Measuring the diagram to some scale, we find that OA = 2.6 cm and OC = 5.4 cm
   We know that

5.4

2.08

2.6

C

A

v OC

vOA

===

∴ Velocity of C,

vC = vA × 2.08 = 5 × 2.08 = 10.4 m/s Ans.

EXERCISE 22.1

1. The ends A and B of a link 1.5 m long are constrained to move in vertical and horizontal
   guides as shown in Fig. 22.6.
   At a given instant, when A is 0.9 m above C it was moving at 3 m/s upwards. Find the
   velocity of B at this instant. (Ans. 2.25 m/s)

Fig. 22.6 Fig. 22.7

Fig. 22.5.